A note on Robinson-Ursescu and Lyusternik-Graves theorem

0395288 - MÚ 2014 RIV NL eng J - Článek v odborném periodiku
Cibulka, R. - Fabian, Marián
A note on Robinson-Ursescu and Lyusternik-Graves theorem.
Mathematical Programming. Roč. 139, 1-2 (2013), s. 89-101. ISSN 0025-5610. E-ISSN 1436-4646
Grant CEP: GA ČR(CZ) GAP201/11/0345
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: open mapping * restrictive metricregularity * graves theorem
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 1.984, rok: 2013
http://link.springer.com/article/10.1007%2Fs10107-013-0662-z

The aim of this note is twofold. First, we prove an analogue of the well-known Robinson–Ursescu Theorem on the relative openness with a linear rate (restrictive metric regularity) of a multivalued mapping. Second, we prove a generalization of Graves Open Mapping Theorem for a class of mappings which can be approximated at a reference point by a bunch of linear mappings. The approximated non-linear mapping is restricted to a closed convex subset of a Banach space.
Trvalý link: http://hdl.handle.net/11104/0223354